There are actually a lot of important elements to consider when constructing a basement, but the two most important are health and safety.  You need to make sure the basement is structurally sound, and you need to make sure that it is water-tight.  Moisture in the basement from lack of proper sealing can cause damage to your entire house.  It can also cause mold to grow, which in turn can be a factor in breathing problems.  Before building a basement, be sure to check building codes and make sure you have permits just like when building a house.  It is obviously easier to build the basement before the house is built but after the plans are drawn.